A quasi-periodic harmonic balance method (HBM) coupled with a pseudo arc-length continuation algorithm is developed and used for the prediction of the steady-state dynamic behaviour of rotor-stator contact problems. Quasi-periodic phenomena generally involve two incommensurable fundamental frequencies, and at present, the HBM has been adapted to deal with cases where those frequencies are known. The problem here is to improve the procedure in order to be able to deal with cases where one of the two fundamental frequencies is a priori unknown, in order to be able to reproduce self-excited phenomena such as the so-called quasi-periodic partial rub. Considering the proposed developments, the unknown fundamental frequency is automatically determined during calculation and an automatic harmonic selection procedure gives both accuracy and performance improvements. The application is based on a Jeffcott rotor model, and results obtained are compared with traditional time-marching solutions. The modified quasi-periodic HBM appears one order of magnitude faster than transient simulations while providing very accurate results.